From Förberedande kurs i matematik 1

The tangent value of the angle \displaystyle 2\pi/7 is the slope of the line which makes an angle \displaystyle 2\pi/7 with the x -axis.

From the figure, we see that the angle between \displaystyle \pi/2 and \displaystyle 2\pi which gives a line with the same slope as the angle \displaystyle 2\pi/7 is \displaystyle v = 2\pi/7 + \pi = 9\pi/7\,.